On the rank of skew-symmetric and general tensors.

The theorem of Alexander and Hirschowitz computes the generic rank of symmetric complex tensors. There is a general pattern, with a list of exceptions. We report about the analogous problem for skew-symmetric and general tensors. There are again some lists of exceptions to the general pattern, and conjectures that such lists are complete. This is joint work with H. Abo and C. Peterson.